The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth BooksMacmillan, 1886 - 400 Seiten |
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Seite 7
... , AB , BC are equal to one another . Wherefore the triangle ABC is equilateral , and it is described on the given straight line AB . [ Axiom 1 . [ Def . 24 . Q.E.F. PROPOSITION 2. PROBLEM . From a given point to draw.
... , AB , BC are equal to one another . Wherefore the triangle ABC is equilateral , and it is described on the given straight line AB . [ Axiom 1 . [ Def . 24 . Q.E.F. PROPOSITION 2. PROBLEM . From a given point to draw.
Seite 8
... Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Q.E.F. PROPOSITION 3. PROBLEM . From the greater of two given straight lines to cut off a part equal to the less Let AB and C be ...
... Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Q.E.F. PROPOSITION 3. PROBLEM . From the greater of two given straight lines to cut off a part equal to the less Let AB and C be ...
Seite 9
... Wherefore from AB the greater of two given straight lines a part AE has been cut off equal to C the less . Q.E.F. PROPOSITION 4 . THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , and ...
... Wherefore from AB the greater of two given straight lines a part AE has been cut off equal to C the less . Q.E.F. PROPOSITION 4 . THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , and ...
Seite 13
... Wherefore , on the same base & c . Q.E.D. * PROPOSITION 8. THEOREM . 256 If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal , the angle which is contained by ...
... Wherefore , on the same base & c . Q.E.D. * PROPOSITION 8. THEOREM . 256 If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal , the angle which is contained by ...
Seite 14
... Wherefore , if two triangles & c . Q.E.D. PROPOSITION 9. PROBLEM . To bisect a given rectilineal angle , that is to divide it into two equal angles . Let BAC be the given rectilineal angle : it is 14 EUCLID'S ELEMENTS .
... Wherefore , if two triangles & c . Q.E.D. PROPOSITION 9. PROBLEM . To bisect a given rectilineal angle , that is to divide it into two equal angles . Let BAC be the given rectilineal angle : it is 14 EUCLID'S ELEMENTS .
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ABCD angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC BC is equal bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore